Any and all graded activities you currently employ in person you can do online. Research papers, quizzes, presentations, group projects, exams, ..... Even pop quizzes - this works best when you have regularly scheduled synchronous meetings. You can break off during the online meeting for the pop quiz within your LMS or you could start/end the online meeting with a pop quiz.
What is particularly important to consider is the value of self testing. Providing opportunities for students to test their level of mastery throughout a course can be the key to learning and subsequent mastery of course content. As an article pertaining to the value of testing points out
"Taking a test is not just a passive mechanism for assessing how much people know, according to new research. It actually helps people learn, and it works better than a number of other studying techniques."
The very first time you teach fully online, simple is elegant. Keep the assessment strategy manageable for you. Don't try to employ many new things you've never done before. As you become more adept at managing the various online tools available you can diversify the type and quantity of assignments, activities, tests, quizzes, .... you will use to grade students.
Recognizing that in an online environment there will be no oversight for exams, strategies to discourage and minimize cheating need to be considered. If keeping all testing fully online, at least randomize the presentation of material and then check the log provided by your LMS. It will typically include enough information (IP address, time stamps for input) for you to detect some types of cheating (e.g. working together). It is also possible to require that the exams be taken under supervision. More and more public and private institutions are providing proctoring services to accommodate online courses. If the course enrolls primarily SJSU students you could reserve a computer lab on campus and proctor exams that are taken online but in person.
The same principles you apply in deciding when, how, and how often to schedule exams and quizzes when teaching in person should be applied in an online setting. The medium through which content is delivered should not impact decisions of this nature. It's still a matter of the rhythm and pattern of the course and its content.